Edexcel IGCSE Math B 9 trigonometry

Use this Trigonometry hub to move from sine, cosine and tangent into bearings, non-right triangles, 3D diagrams and multi-step geometry problems.

Covered syllabus points

9.A Sine, cosine and tangent 9.B 2D and 3D trigonometry 9.C Elevation and depression 9.D Bearings

[Maximum number: 3]

Diagram NOT accurately drawn

Figure 3 shows a circle with centre O and radius 10 cm.
The points A and B lie on the circle such that $\angle A O B=100^{\circ}$ The point C is such that AC and BC are tangents to the circle.

Calculate the length, in cm to 3 significant figures, of BC.

One correct method:
$\tan40^\circ=\frac{10}{BC}$
Equivalently:
$\tan50^\circ=\frac{BC}{10}$
Hence:
$BC=10\tan50^\circ=11.9175\ldots$
Final answer:
$11.9\text{ cm}$

[Maximum number: 7]

Figure for Question 9 Trigonometry question 2 — Edexcel IGCSE Math B

Figure 3 shows a solid right prism ABCDEFGH.
Diagram NOT accurately drawn.
The base of the prism, ABCD, is a rectangle and is horizontal. Trapezium BCHG is a cross section of the prism.
$AB=4\text{ m},\quad BC=3\text{ m},\quad CH=2.4\text{ m},\quad GB=1.5\text{ m}$ $\angle GBC=\angle BCH=\angle ABG=\angle DCH=90^\circ$

(a)

Calculate the angle of depression, in degrees to one decimal place, of G from E.

[ 3 ]

Horizontal diagonal:
$DB=\sqrt{4^{2}+3^{2}}=5$
Vertical difference:
2.4-1.5=0.9 $\tan\theta=\frac{0.9}{5}$
Final answer:
$10.2^\circ$
An answer of $79.8^\circ$ gains 2 marks.

(b)

The point P lies on the line GH such that $GP=\frac23GH$ .
The point Q lies on the line BC such that $BQ=\frac23BC$ .
Calculate, in degrees to one decimal place, $\angle APQ$ .

[ 4 ]

$PQ=1.5+\frac23(2.4-1.5)=2.1$ $AQ=\sqrt{4^{2}+2^{2}}=\sqrt{20}$ $\tan\angle APQ=\frac{\sqrt{20}}{2.1}$
Final answer:
$64.8^\circ$
Only allow $65^\circ$ from correct working.

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Covered syllabus points

9 Trigonometry question 1

9 Trigonometry question 2

Question (a)

Question (b)